Learning Curve Effect

200 MC=20Q ATC=1,000Q –1+10Q

AVC=10Q

0 10 Q

FIGURE 6.3

minimized where Q = 0.Substituting this into the AVC equation,we obtain

In other words,at zero output the firm incurs only fixed cost,that is,

Again,the marginal cost equation is

Marginal cost at Q* = 0 is

Again,not surprisingly, MC = AVC at the output level that minimizes

AVC. c.Figure 6.3 diagrams the answers to parts a and b.

AVC = () = 100 0

TC TFC = + () =1000 100 2 ,

MC Q = 20

MC = () = 200 0

LEARNING CURVE EFFECT

The discussion in Chapter 5 noted that the profit-maximizing firm will operate in stage II of production.It will be recalled that in stage II the marginal product of a factor,say labor,is positive,but declining at an increasing rate.The phenomenon is a direct consequence of the law of diminishing marginal product.At constant factor prices this relationship implies that as output is expanded,the marginal cost of a variable factor increases at an increasing rate.

An important assumption implicit in the law of diminishing marginal product is that the quality of the variable input used remains unchanged.

TABLE 6.1 Learning Curve Effects:Unit Labor Costs

Output m = 0.9 m = 0.8 m = 0.7

1 $10,000.00 $10,000.00 $10,000.00 2 9,000.00 8,000.00 7,000.00 4 8,100.00 6,400.00 4,900.00 8 7,290.00 5,120.00 3,430.00 16 6,561.00 4,096.00 2,401.00 32 5,904.90 3,276.80 1,680.70 64 5,314.41 2,621.44 1,176.49 128 4,782.97 2,097.15 823.54 256 4,340.67 1,677.72 576.48

In the case of labor,for example,the “productivity”of labor is assumed to remain unchanged regardless of the level of production.In fact,this restriction is an oversimplification:it is reasonable to expect that as output expands over time,the typical laborer “gets better”at his or her job.In other words,it is reasonable to assume that workers become more productive as they gain experience.This would suggest that over some range of production,per-unit labor input might,in fact,fall.At constant labor prices,this implies that per-unit labor costs may in fact fall.

We are not,of course,talking about stage I of production,where per-unit costs fall because of increased specialization as additional units of,say,labor are added to underutilized amounts of capital.On-the-job training and experience will make workers more productive,which has important implications for the cost structure of the firm.It is precisely the expectation of greater productivity that compels many firms to underwrite on-site employee training and off-site continuing education programs.The relationship between increased per-worker productivity and reduced perworker cost at fixed labor prices associated with an increase in output and experience is called the learning curve effect.

Definition: The learning curve effect measures the relation between an increase in per-worker productivity (a decrease in per-unit labor cost at fixed labor prices) associated with an improvement in labor skills from onthe-job experience.

One measure of the learning curve effect is G= Per-unit labor cost= jQb (6.17) where j is the per-unit cost of producing the first unit of output, Q is the level of output, b= (ln m)/(ln l), m is the learning factor,and l is a factor of output proportionality.In fact, b is a measure of the learning curve effect. It determines the rate at which per-unit labor requirements fall given the rate at which workers “learn”(m) following a scalar (proportional) increase in production (l).The value of m varies from zero to unity (0 £ m £ 1).As

the value of m approaches zero,the learning curve effect on lowering perunit labor costs becomes more powerful.

Table 6.1 presents data for 90% (m = 0.9),80% (m = 0.8),and70% (m = 0.7) learning curves for a factor of output proportionality (l) of 2.That is,each time output is doubled,the per-unit labor cost drops to become 90, 80,or 70% of its previous level.It is assumed that it takes 1,000 labor units (say,labor hours) to produce the first unit of output,and that the wage rate is constant at $10 per hour.Thus,the per-unit labor cost of producing the first unit of output is $10,000.If the learning factor is m = 0.9 (i.e.,the learning process is relatively slow),the per-unit labor cost when Q = 2 is $9,000. When Q = 4,per unit labor cost is $8,100,and so on.

The reader will note that the lower the learning factor (i.e.,the quicker the learning process),the more rapidly per-unit labor costs fall as output expands.Since the wage rate in this example is constant at $10 per hour, the learning curve effect implies that fewer labor units per unit of output are required as output increases.The extreme cases are m = 1 and m = 0. When m = 1,no learning whatsoever takes place,and b= (ln1/ln l) = 0.In this case,there are no learning curve effects,and the per-unit labor cost remains unchanged.On the other hand,when m = 0,then b=-•.In this case,learning is so complete and production so efficient that the per-unit labor cost reduces to zero,which implies that at a constant wage rate no labor is required at all.In the two-input case,this suggests that all production technology is embodied in the amount of capital employed.

Learning curve effects are usually thought to result from the development of labor skills,especially for tasks of a repetitive nature,over time. More broadly,however,incremental reductions in per-unit labor costs may result from a variety of factors,such as the adoption of new production, organizational,and managerial techniques,the replacement of higher cost with lower cost materials,an new product design.Consideration of these additional factors has given rise to the broader term experience curve effects.

Definition:The experience curve effect is a measure of the relationship between an increase in per-worker productivity (a decrease in per-worker cost at fixed labor prices) associated with an improvement in labor skills from on-the-job experience,the adoption of new production,organizational and managerial techniques,the replacement of higher cost with lower cost materials,new product design,and so on.

Problem 6.4. Suppose that the labor cost to a firm of producing a single unit of output is $5,000. a.If the learning factor is 0.74 and the factor of proportionality is 2.5, estimate the per-unit labor cost of producing 120 units of output. b.If the wage rate is constant at $15 per hour,how many labor hours are required to produce the first unit of output? How many labor hours are required per unit of output when 120 units are produced?